Question: Simplify the following expression: $t = \dfrac{-36z}{-24z^2 - 66z}$ You can assume $z \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-36z = - (2\cdot2\cdot3\cdot3 \cdot z)$ The denominator can be factored: $-24z^2 - 66z = - (2\cdot2\cdot2\cdot3 \cdot z \cdot z) - (2\cdot3\cdot11 \cdot z)$ The greatest common factor of all the terms is $6z$ Factoring out $6z$ gives us: $t = \dfrac{(6z)(-6)}{(6z)(-4z - 11)}$ Dividing both the numerator and denominator by $6z$ gives: $t = \dfrac{-6}{-4z - 11}$